X-ray apparatus and method



June 13, 1950 H. EKSTEIN ETI'AL 2,511,151

x-RAY' APPARATUS AND METHOD Filed Sept. 24, 1947 fl ms' [A19 72-7 latented June 13, 1950 UNITED STATES PATENT OFFICE X-RAY APPARATUS ANDMETHOD Hans Eiistein and Stanley Siegel, Chicago, 111., assignors toArmour Research Foundation of Illinois Institute of Technology, Chicago,111., a corporation of Illinois Application September 24, 1947, SerialNo. 775,824

7 Claims. (Cl. 25053) This invention relates to an improved method andapparatus for facilitating the precision determination of latticeparameters, and particularly to a method and apparatus for effecting thefocusing of a beam of X-rays upon an X-ray sensitive indicating mediumafter diffraction of such beam by a sample to be analyzed.

The desirability of producing a focusing of X-rays to facilitate X-rayanalysis of crystalline structure is in itself not a new concept;however, all previous methods utilized were based on geometricalfocusing in which supposedly mono chromatic X-rays are brought to afocus. However, at large angles of diffraction, which are particularlydesirable in precision lattice determinations, such as in phase studies,stress measurements, etc., the diffraction line becomes inevitably broadbecause of the finite spectral width of the characteristic radiation andbecause of the diffraction mechanism.

In contrast, the methods and apparatus constituting this invention arebased upon the concept of producing a focusing of X-rays of difierentwavelengths. Hence, the methods and apparatus of this invention permitthe determination of lattice parameters with improved accuracy by makingthe Debye-Scherrer line sharper than is possible by any methodheretofore known.

The deficiencies of the presently known methods will be clearly apparentfrom the following analysis. The limiting factor of the precisionpossible by conventional focusing methods is the finite spectral widthof the characteristic X-ray line. A strictly parallel and monochromaticbeam, when striking a crystal aggregate of sufficiently large grains,will give rise to a diffracted beam of negligible angular width. As itis not possible to produce a characteristic X-ray line of a singlewave-length, and since such characteristic X-ray line consists of afinite band of wavelengths, it follows that under the usual conditionsthe resulting diffracted beam cannot give rise to a line any narrowerthan that corresponding to the spectral width of the initial beam.

It is true that other factors, the geometric conditions and the smallsize of crystal grains, usually cause a broadening of the line in excessof that due to the spectral impurity of the incident radiation; but atlarge Bragg angles 0 of the diffraction, where the Bragg angle 0 has thelargest sensitivity to changes in lattice parameters, the width causedby thisspecial impurity is predominant when the geometric arrangementsare as refined as currently feasible.

In other words, no further refinement of the geometry of the system canproduce a line substantially narrower than those currently obtained.

v Accordingly, the methods and apparatus embodied in this inventionprovide a decided improveinent in the focusing of X-rays through theattainment of an indicating line substantially narrower than thosecurrently obtained, by elimihating the line broadening efiects caused bythe spectral impurity. The methods and apparatus of this inventioncontemplate the utilization of a diverging beam of X-rays including aband of wavelengths and a portion of the rays of each distinctwavelength are caused to pass through a predetermined focal point afterdiffraction by a polycrystalline sample being analyzed. If an Iii-raysensitive film or other recording instrument is placed at such focalpoint, the resulting line indication will be very narrow and henceadaptable for precision X-ray analysis purposes.

Accordingly, it is an object of this invention to provide an improvedmethod and apparatus'for X-ray analysis of crystal structure, andparticularly a method and apparatus for producing a sharper focus ofX-rays diffracted by a polycrystalline sample than has heretofore beenpossible of accomplishment.

Another object of this invention is the provision of an improved methodand apparatus for focusing of X-rays which does not require amonochromatic beam of X-rays for its successful operation but which willproduce a sharp focus of a beam of X-rays of a finite band ofwavelengths.

Still another object of this invention is to provide a method andapparatus for focusing of an X-ray beam deflected by a polycrystallinesample wherein large Bragg angles of incidence of the X-rays upon thepolycrystalline sample may be employed without reducing the sharpness ofthe focus achieved.

A particular object of this invention is to provide an improved X-raytube envelope construce tion particularly adapted for producing a beamof X-rays of such characteristics that the diffraction of such beam by apolycrystalline sample located exteriorly of the tube envelope willautomatically produce a focusing of the diffracted beam, andparticularly a shielding envelope construction J which may beconveniently adjusted to produce such focusing for any one of aplurality of dis? tinct bands of X-ray wavelengths.

The specific nature of this invention, as well as other objects andadvantages thereof, will become apparent to those skilled in the artfrom the following detailed description taken in conjunction with theannexed sheet of drawings, which, by way of preferred example only,illustrates two embodiments of this invention.

On the drawings: 7

Figure 1 is a schematicview of an X-ray focusing system illustrating thefundamental concept employed in accordance with this invention to ob:tain focusing of an X-ray beam after diffraction 60 by a polycrystallinesample;

Figure 2 is a schematic sectional view illustrating one arrangement ofan X-ray tube and shielding jacket for producing X-ray focusing inaccordance with this invention;

Figure 3 is a transverse sectional view taken on the plane IIII II ofFigure 2 and Figure 4 is a schematic sectional view illustrating amodified construction of an X-ray tube and jacket for producing focusingof X-rays-by the principles of this invention.

As shown on the drawings:

Referring to Figure 1, let it be assumed that at the point P a source ofX-rays is located which produces a diverging original beam of X-raysIll. The beam I preferablycomprises a finite band of wavelengths andthis condition will be recognized by'those skilled in the art asparticularly easy to fulfill inasmuch as'that is the type of radiationcommonly achieved from any particular point on the target of aconventional X-ray tube. In any event, let it be assumed that thecentral ray ID of the diverging beam ID has a wavelength A.

Now, in accordance with this invention, the divergent, multi-wavelengthbeam I0 is permitted to strike a plain crystal face such as thatprovided by a monochromator II. It will be recognized that a diffractedor reflected beam I2 will thereupon be produced. However, the beam I2will be divergent and will have the further characteristic that everyray in a particular angular portion of the beam I2 will have only onewavelength because it has been diffracted under an angle of diffractiondifferent from any other ray. This phenomenon is readily apparent fromconsideration of the fundamental law of X-ray diifraction which iscommonly set forth in the following equation:

A=2dm sin 0 (1) where A is a particular wavelength diffracted, dm is theatomic spacing in the difiracting material and 0 is the glancing angleof the radiation of wavelength A with respect ,to the crystal producingthe diffraction. The angle 0 is commonly referred to as the Bragg angle.

The difiracted beam I2 produced by the monochromator I I .is thereforeformedofrays whose angular position with respect to the central ray I2of wavelength A is a function of the difference in wavelength of each ofthe particular rays and the central ray I2. Thus the ray I2a at one sideof the beam I2 is angularly spaced from the central ray I2 by the angledo, and the wavelength of such ray I2a may be A plus 11A. The ray [21)at the other edge of the beam is angularly spaced from the central rayI2 of wavelength A byan angle of minus d0, and the wavelength of this.ray is A minus dA.

The beam I2 is then permitted to strike thesurface of a polycrystallinesample I3 which is to be analyzed. With such aspatial distribution ofthe various wavelengths forming the diffracted ray l2, it is obviousthat each ray of the beam I2 will be diffracted by the polycrystallinesample only if it meets a crystal grain suitably oriented, thisorientation being different for each incident ray. The various orientedcrystals for the required diffraction of the central ray I2 as well asthe edge rays I2a and |2b are respectively indicated by the lines I3,I3a and I3b. When such diffraction occurs, the resulting diffractedrays, respectively represented by I4, I la and Nb, will no longer bedivergent but will be convergent, and under certain circumstances suchdiffracted rays can be made to intersect approximately at a point F.

Therefore, if an X-ray sensitive film or other recording or indicatinginstrument is placed at the point F, then the line indication producedon such film will be very sharp, and precise determinations may be madeof the lattice parameters of the polycrystalline sample I3.

Geometrical analysis will indicate not only the conditions under whichsuch focusing of the beam diffracted by the polycrystalline sample willoccur at the point Fbut also the location of the point F with respect tothe point source P and the monochromator I I. The geometrical analysisproceeds as follows:

Still utilizing Figure 1, let P represent the apparent source of theX-ray beam I2 as viewed from the polycrystalline sample I3.

Let dm be the atomic spacing in the monochromator 'I I; (in be-the Braggangle for the centralray I0 diffracted by the monochromator II; (is bethe atomic spacing in the polycrystalline sample I3; and 0s be'the Braggangle for the central ray I2 of wavelength A diffracted by thepolycrystalline sample I3.

Then by Braggs law, the diffraction of the central ray of wavelength Awhich occurs by the monochromator I I may be represented bythe followingequation:

sin gm Likewise, the diffraction of the same ray by the polycrystallinesample I3 at the point E may be represented by:

S1110: Considering aray of slightly different wavelength and diffractionangle, i. e., A+dA and 0+d0, 'we obtain by differentiating (2) and (3)and setting equals against equals rim COS0md0m=ds cos 681108 d,, cos 0,,d9. d0, By geometric analysis, the angle ,HFE=2d0,-|-d0m (5) Letthedistance fromthe .point source ,P to the sample I3 measuredalong thepath of the .central ray of wavelength A (which, of course, is thedistance PfE) equallL, .and the distance frompoint E onsampleI3Vto,focus. point F equal Then from .the geometry ofFigure 1,

1' (angle HFIQ It has therefore been demonstrated that the location ofthe focusing point F as measured by the distance along the central rayof lavelength A from the polycrystalline sample I3 may be definitelycomputed for any selected wavelength and Bragg angle relationship of theX-ray beam with respect to the monochromator II and the polycrystallinesample I3.

It should be particularly noted that the most desirable dimensionalrelationships are obtained at Bragg angle approaching 90.

For values of s approaching 90 and 08 01, it will be observed that theratio of the total distance between the point source P and thepolycrystalline sample I3 traversed by the central ray to the distanceof the focusing point F from the sample It as measured along the pathtraversed by the central ray is equal to 3. Hence-very practicaldimensional relationship can be obtained at Bragg angles approaching 90,for if the. distance from the sample I3 to the focal point F is selectedas 5 cm., then the distance L traversed by the central ray need only be15 cm., which is an entirely practical arrangement. For lower Braggangles 0m it may be readily observed that the ratio of L/f increasesrapidly and hence results in less practical spatial positioning of thesource of X-rays P with respect to the monochromator II and the sampleI3.

Referring now to Figures 2 and 3, there is shown schematically anapparatus for conveniently utilizing the X-ray focusing methodsheretofore disclosed. Thus a shielding jacket 20 is provided insurrounding relationship to a focusing X-ray cathode 2| and target anode22. That portion of the surface of target anode 22 upon which the highvelocity electrons impinge may, if desired, have a removable target 23mounted thereon in conventional fashion. Thus, by selection of thematerial of the removable target 23, it is'possible to obtain a varietyof discrete bands of wavelengths of the resulting X-rays. Themonochromator I I is then mounted in any convenient fashion within theshielding jacket 20 and in such position as to receive a beam of X-raysemitted from a point or line P of the target surface at a large Braggangle of incidence.

The electrons are brought to a focus on the target point P by use of anysuitably sharp focusing arrangement. The shape of the focus on the pointP may be in the form of a point or line, or any other suitably shapedsharp focus. The electron source is within the cathode 2|. Apparatus isprovided to permit the angular position of the monochromator II to beadjusted with respect to the target 23, and such adjustment permits theapparatus to be conveniently adapted to employ any one of a largevarietyof wavelength bands of X-rays.

The shielding jacket 20 is provided with a window portion 20a capable oftransmitting X-rays therethrough which is disposed opposite themonochromator II and in selected spatial arrangement therewith so thatall diifracted beams from the monochromator I I will pass through thewindow 20a to the exterior of the jacket 20. The polycrystalline sampleI3 to be analyzed is disposed exteriorly of the jacket 20 in the path ofthe diffracted beam from the monochromator II. A focusing of the raysdiffracted by the polycrystalline sample I 3 will then be obtained at apoint, such as F, exteriorly of the jacket 20 and hence permitsconventional X-ray recording and/or indicating equipment (not shown) tobe positioned at this point.

In the modified arrangement shown in Figure 4, the shielding jacket 20is provided with two X-rays transmitting windows 20b and 200,respectively. The monochromator I I is then positioned to the exteriorof the jacket 20 and adjacent the X-ray transmitting Window 20b so thatan original beam of X-rays produced from a point P on the target 23 willpass through the window 20b and impinge upon the monochromator II. Thediffracted beam then passes through the window 20b in the reversedirection and traverses the interior of jacket 20 to pass through thesecond X-ray transmitting window 200 and then strike the polycrystallinesample I3 again disposed on the exterior of the jacket 20. Thediffracted beam from the sample I3 may then be brought to a focal pointF exteriorly of the jacket 20.

It should be particularly noted thatin both embodiments of the preferredforms of apparatus for effecting the focusing of X-rays in accordancewith this invention, Bragg angles of diffraction approaching areutilized both in the diffraction by the monochromator II and by thepolycrystalline sample I3, and further, the focusing of the X-rays isaccomplished without interference of the various diffracted beams witheach other. Any other beams originating on the target anode willlikewise produce very little inter--v ference efiects.

It is therefore apparent that the method and apparatus of this inventionprovides an unusually simple yet highly precise method of accomplishingthe focusing of an X-ray beam including a distinct band of wavelengthsand, as a result, the accuracy of X-ray analysis has been substantiallyimproved without requiring apparatus of any greater expense orcomplexity than that conventionally employed in the known methods to produce inferior results.

It will, of course, be understood that various details of constructionand application may be modified through a wide range without departingfrom the principles of this invention, and it is, therefore, not thepurpose to limit the patent granted hereon otherwise than necessitatedby the scope of the appended claims.

We claim as our invention:

1. The method of X-ray analysis which comprises producing apolychromatic beam of X-rays diverging from a substantially point sourceand having a central ray of wavelength A, disposing a flat face of acrystal in the path of said beam to produce a reflected beam, wherebythe reflected beam is angularly divergent from said central ray but hasa frequency distribution proportional to the angular separation fromsaid central ray, disposing a polycrystalline sample in the path of saidreflected beam of X-rays, thereby producing a second reflected beam, andlocating an X-ray sensitive indicating medium in the path of said secondreflected beam and at a predetermined distance from said sample measuredalong the path of said central ray of wavelength A of said secondreflected beam, said predetermined distance being equal to -L cos 20.tan 0, 1+2 tan 0,,

where L equals the sum of the distances from the source of the X-rays tothe polycrystalline sample measured alon the path of said central ray ofwavelength A, 6111 is the Bragg angle for said central ray of wavelengthA difiracted by the crystal, and 05 is the Bragg angle for said centralray of wavelength A difiracted by the polycrys-l talline-sample.

-2. The method of X-ray analysis which comprises producing apolychromatic beam of X-rays from apoin-t source having a central ray ofWave ength A, placing a flat face of a crystal in the path of t e beam,locating a sample to be analyzed in the path of the diffracted beam, and

positioning an X-ray sensitive indicating medium in the path of theX-ray beam diffracted by the sample at a distance from the sample, equalto -L cos 26,

3. The method of focusing a polychromatic beam of X-rays having acentral ray of wavelength A which beam is reflected from apolycrystalline sample Which comprises arranging the fiat face of acrystal monochromator intermediately between the source of thepolychromatic X-ray beam and. the sample so that the polychromatic X-raybeam incident upon the sample is initially diffracted by saidmonochromator, and positioning the sample with respect to themonochromator so that the ratio of the total distance traversed by thecentral. ray of wavelength A from the source to the sample to thedistance from. the sample to the desired focal point measured along thepath of the central ray of wavelengthA equals tan 0,, 1 tan 0,,,)( cos20,

where m is the Bragg angle for the central ray of wavelength A reflectedby the monochromator; and 05 is the Bragg angle for the central ray ofWavelength A reflected by the sample.

4. The method of focusing a polychromatic beam of X-rays reflected froma polycrystalline sample and having a central ray of wavelength A whichcomprises arranging a flat face of a crystal immediately between thesource of the polychromatic beam of X-rays and the sampleso that the Xray beam impinging onthe sample is initially reflected by said crystalat a Bragg angle approaching 96", and positioning the sample withrespect to the said crystal and the source of the X rays so that theratio of the total distance traversed b the central ray of wavelength Afrom the source to the sample to the distance from the Sample measuredalong the path of the central ray of wavelength A at which focusing ofthe beam is desired, equals tan l9 1 tan 0,, cos 29,

where 0m is the Bragg angle for the central ray of wavelength Areflected by the crystal, and 5s is the Bragg angle for the central rayof wavelength A reflected by the polycrystalline sample.

5. Apparatus for X-ray analysis comprising a.

source of diverging, polychromatic X-rays producing a beam having acentral ray of wavelength A, a flat faced, crystal monochromator,

means for adjustably positioning said crystal the pathot; said divergingreflected beam, thereby producing a converging reflected beam of X-rays,and an 'X-ray sensitive indicating medium disposedin the path of saidsecond reflected beam at av predetermined distance from said samplemeas-. ured; along the path of said central ray or wavelength A equal to,L cos 2Q,

where hequals the sum of the distances from the source of X-rays to thesample measured along the path of the central ray of wavelength A, @m isthe Bragg angle for the central ray of wavelength A reflected by themonochromator, and 05 is the Bragg angle for the central ray ofwavelength A reflected by the polycrystalline 4 9 6, Apparatus forX.-ray analysis comprising a "tube envelope enclosing a source of a.beam. of

polychromatic X-rays, said envelope having. a first X-ray transmittingwindow therein permitting, abeam of X-rays to pass through saidenvelope, a. monochrcmator disposed in the path of said polychromaticbeam and arranged to pro.- duce a first reflected beam of polychromaticX- rays directed through said first window back into said envelope, saidenvelope having a second X- .ray transmitting window disposed in thepath of said first reflected beam, means for positioning. apolycrystalline sample. exteriorly of said; en- Velope and in the pathofsaid first reflected beam, thereby producing a second reflected beam,and

,, an X-ray sensitive recording medium locatediin the path of saidsecond reflected medium at a.

predetermineddistance from said sample corresponding to. the location ofa focal point of said second reflected beam.

7. Apparatus for X-ray analysis comprising a tube envelope enclosing asource of a beam of polychromatic X-rays having a central ray ofvwavelength, A, said envelope having afirst X-ray transmitting window,therein permitting saidpolychromatic. beam of X-rays to pass throughsaid envelope, amonochromator disposed inv thepath of saidebeamandarranged to produce a first reflected polychromatic beam ofX-raysdirected through s id first window into said envelope, saidenvelope having a second X-ray transmitting window disposed in the pathof said first reflected beam, means for positioning a polycrystallinesampleexteriorly of said; envelope and in the path of said firstreflected beam, thereby producing a second reflected beam, and an X-raysensitive recording medium located in the path of. said second reflectedmedium at a distance from saidsample measured along the path of saidcentral ray of-wavelength A equal to L cos 20,

where 1; equals the sum of the distances fromthe source of the X-rays tothe sample and is meas ured along the path of the central ray of.Wavelength A, where .6111 is the Bragg angle for the centralray. ofwavelength A reflected by the monochromator and is the Bragg angle forthe central ray of wavelength A reflected by the polycrystalline sample.

HANS EKSTEIN.

STANLEY SIEGEL.

' (References on following page).

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,626,306 St. John Apr. 26, 19272,329,320 Atlee Sept. 14, 1943 2,452,045 Friedman Oct. 26, 1948 OTHERREFERENCES X-Rays and Electrons, by A. H. Compton, pp. 133 and 134, D.Van Nostrand Co., New York, 1926. (Copy in Div. 54.)

